This is what allows pifs to work!
this post was submitted on 26 Dec 2024
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I can't tell if this is a joke or real code... like for this sentence below.
The cat is back.
Will that repo seriously run until it finds where that is in pi? However long it might take, hours, days, years, decades, and then tell you, so you can look it up quickly?
Thats very cool. It brings to mind some sort of espionage where spies are exchanging massive messages contained in 2 numbers. The index and the Metadata length. All the other spy has to do is pass it though pifs to decode. Maybe adding some salt as well to prevent someone figuring it out.
It has not been proven either way but if pi is proven to be normal then yes. https://en.m.wikipedia.org/wiki/Normal_number
no. it merely being infinitely non-repeating is insufficient to say that it contains any particular finite string.
for instance, write out pi in base 2, and reinterpret as base 10.
11.0010010000111111011010101000100010000101...
it is infinitely non-repeating, but nowhere will you find a 2.
i've often heard it said that pi, in particular, does contain any finite sequence of digits, but i haven't seen a proof of that myself, and if it did exist, it would have to depend on more than its irrationality.
Isnt this a stupid example though, because obviously if you remove all penguins from the zoo, you're not going to see any penguins
Its not stupid. To disprove a claim that states "All X have Y" then you only need ONE example. So, as pick a really obvious example.
It's misunderstanding the question even if unintentionally.
Clearer: Since Pi is infinite and non-repeating, would that mean any finite sequence of non-repeating digits from 0-9 should appear somewhere in Pi in base 10?
They somehow interpreted it as Does any possible string of infinite non-repeating digits contain every possible finite sequence of non repeating digits?
It's like if I ask "since the dictionary contains every word that means it contains every letter right?" And someone answers, actually you'll find if you translate it to Japanese and only use kanji it actually doesn't contain these letters. It fundamentally isn't what I'm asking, and yes, you can argue I didn't say IN ENGLISH, but just like the pi question, I feel like it's pretty intuitive that I wasn't referring to non English letters in the question.
In terms of formal logic, this...
Since Pi is infinite and non-repeating, would that mean any finite sequence of non-repeating digits from 0-9 should appear somewhere in Pi in base 10?
...and this...
Does any possible string of infinite non-repeating digits contain every possible finite sequence of non repeating digits?
are equivalent statements.
The phrase "since X, would that mean Y" is the same as asking "is X a sufficient condition for Y". Providing ANY example of X WITHOUT Y is a counter-example which proves X is NOT a sufficient condition.
The 1.010010001... example is literally one that is taught in classes to disprove OPs exact hypothesis. This isn't a discussion where we're both offering different perspectives and working towards a truth we don't both see, thus is a discussion where you're factually wrong and I'm trying to help you learn why lol.
The explanation is misdirecting because yes they're removing the penguins from the zoo. But they also interpreted the question as to if the zoo had infinite non-repeating exhibits whether it would NECESSARILY contain penguins. So all they had to show was that the penguins weren't necessary.
By tying the example to pi they seemed to be trying to show something about pi. I don't think that was the intention.
It does contain a 2 though? Binary ‘10’ is 2, which this sequence contains?
They also say "and reinterpret in base 10". I.e. interpret the base 2 number as a base 10 number (which could theoretically contain 2,3,4,etc). So 10 in that number represents decimal 10 and not binary 10
I don’t think the example given above is an apples-to-apples comparison though. This new example of “an infinite non-repeating string” is actually “an infinite non-repeating string of only 0s and 1s”. Of course it’s not going to contain a “2”, just like pi doesn’t contain a “Y”. Wouldn’t a more appropriate reframing of the original question to go with this new example be “would any finite string consisting of only 0s and 1s be present in it?”
They just proved that "X is irrational and non-repeating digits -> can find any sequence in X", as the original question implied, is false. Maybe pi does in fact contain any sequence, but that wouldn't be because of its irrationality or the fact that it's non-repeating, it would be some other property
Like the other commenter said its meant to be interpreted in base10.
You could also just take 0.01001100011100001111.... as an example
No, the fact that a number is infinite and non-repeating doesn't mean that and since in order to disprove something you need only one example here it is: 0.1101001000100001000001... this is a number that goes 1 and then x times 0 with x incrementing. It is infinite and non-repeating, yet doesn't contain a single 2.
This proves that an infinite, non-repeating number needn't contain any given finite numeric sequence, but it doesn't prove that an infinite, non-repeating number can't. This is not to say that Pi does contain all finite numeric sequences, just that this statement isn't sufficient to prove it can't.
you are absolutely right.
it just proves that even if Pi contains all finite sequences it's not "since it oa infinite and non-repeating"
That was quite an elegant proof
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https://github.com/philipl/pifs
πfs is a revolutionary new file system that, instead of wasting space storing your data on your hard drive, stores your data in π! You'll never run out of space again - π holds every file that could possibly exist! They said 100% compression was impossible? You're looking at it!
I enjoyed this linked text:
If you compute it, you will be guilty of:
- Copyright infringement (of all books, all short stories, all newspapers, all magazines, all web sites, all music, all movies, and all software, including the complete Windows source code)
- Trademark infringement
- Possession of child pornography
- Espionage (unauthorized possession of top secret information)
- Possession of DVD-cracking software
- Possession of threats to the President
- Possession of everyone's SSN, everyone's credit card numbers, everyone's PIN numbers, everyone's unlisted phone numbers, and everyone's passwords
- Defaming Islam. Not technically illegal, but you'll have to go into hiding along with Salman Rushdie.
- Defaming Scientology. Which IS illegal--just ask Keith Henson.
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